The Australian defender played a crucial role in keeping the Gulls in League Two last season and he has ended speculation over his future.
"I've known Downesy for a long time. I was at Chesterfield with him and he's a good player. Throughout his career, just when it looked like he was going to take off, he's picked up an injury.
"The good thing for him was a clean season last year and I'm quite sure his injuries are over now, and he will go on to be one of the better centre-halves in the league."